Elementary Algebra

by
Kaufmann, Jerome; Schwitters, Karen;

Published by
Cengage Learning

ISBN 10:
1285194055

ISBN 13:
978-1-28519-405-9

Chapter 7 - Algebraic Fractions - Chapter 7 Review Problem Set: 3

Answer

$= \frac{3n+5}{n+2}$

Work Step by Step

$\frac{3n^{2}-n-10}{n^{2}-4}$
1. Factor the numerator:
$= \frac{3n^{2}-6n+5n-10}{n^{2}-4}$
$= \frac{3n(n-2)+5(n-2)}{n^{2}-4}$
$= \frac{(3n+5)(n-2)}{n^{2}-4}$
2. Factor the denominator
Whenever you only see a variable squared (without a coefficient) along with the subtraction of a perfect square, you know that it is a difference of two squares problem. Therefore, you use this shortcut to obtain:
$= \frac{(3n+5)(n-2)}{(n-2)(n+2)}$
3. Cancel out $n-2$ from the denominator and numerator
$= \frac{(3n+5)}{(n+2)}$
$= \frac{3n+5}{n+2}$